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1.
We study correlation functions in topologically twisted , d=4 supersymmetric Yang–Mills theory for gauge groups of rank larger than one on compact four-manifolds X. We find that the topological invariance of the generator of correlation functions of BRST invariant observables is not spoiled
by noncompactness of field space. We show how to express the correlators on simply connected manifolds of b
2,+(X)>0 in terms of Seiberg–Witten invariants and the classical cohomology ring of X. For manifolds X of simple type and gauge group SU(N) we give explicit expressions of the correlators as a sum over =1 vacua. We describe two applications of our expressions, one to superconformal field theory and one to large N expansions of SU(N) , d=4 supersymmetric Yang–Mills theory.
Received: 30 March 1998 / Accepted: 17 April 1998 相似文献
2.
It has been shown in the work of Chakrabarti, Sherry and Tchrakian that the
chiral SO
±(4 p) Yang–Mills theory in the Euclidean 4 p (p≥ 2) dimensions allows an axially symmetric self-dual system of equations similar to Witten's instanton equations in the classical
4-dimensional SU(2)∼SO
±(4) theory and the solutions represent a new class of instantons. However the rigorous existence of these higher-dimensional
instanton solutions has remained open except for the solution of unit charge representing a single instanton. In this paper
we establish an existence and uniqueness theorem for multi-instantons of arbitrary charges in the case p≥ 2. These solutions are the first known instantons, with the Chern–Pontryagin index greater than one, of the Yang–Mills
model in higher dimensions. Our approach is a study of a nonlinear variational equation defined on the Poincaré half plane.
Received: 20 May 1996 / Accepted: 30 April 1997 相似文献
3.
4.
Hyun Seok Yang 《The European Physical Journal C - Particles and Fields》2009,64(3):445-457
We map noncommutative (NC) U(1) gauge theory on ℝ
C
d
×ℝ
NC
2n
to U(N→∞) Yang–Mills theory on ℝ
C
d
, where ℝ
C
d
is a d-dimensional commutative spacetime while ℝ
NC
2n
is a 2n-dimensional NC space. The resulting U(N) Yang–Mills theory on ℝ
C
d
is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang–Mills theory onto ℝ
C
d
. We show that the gauge-Higgs system (A
μ
,Φ
a
) in the U(N→∞) Yang–Mills theory on ℝ
C
d
leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for
d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4{\mathcal{N}}=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system
(A
μ
,Φ
a
) in half-BPS configurations describes self-dual Einstein gravity. 相似文献
5.
A. H. Khater D. K. Callebaut S. M. Sayed 《International Journal of Theoretical Physics》2006,45(6):1021-1028
In this paper, we found a new representation for self-duality . In addition, exact solution class of the classical SU(2) Yang–Mills field in four-dimensional Euclidean space and two exact solution classes for SU(2) Yang–Mills when ρ is a complex analytic function are also obtained.
PACS numbers: 11.15.-q Gauge field theories, 11.15.Kc Semiclassical theories in gauge fields, 12.10.-g, 12.15.-y Yang–Mills fields 相似文献
6.
The field equations of supersymmetric Yang–Mills theory in ten dimensions may be formulated as vanishing curvature conditions
on light-like rays in superspace. In this article, we investigate the physical content of the modified SO(7) covariant superspace constraints put forward earlier [11]. To this end, group-algebraic methods are developed which allow
to derive the set of physical fields and their equations of motion from the superfield expansion of the supercurl, systematically.
A set of integrable superspace constraints is identified which drastically reduces the field content of the unconstrained
superfield but leaves the spectrum including the original Yang–Mills vector field completely off-shell. A weaker set of constraints
gives rise to additional fields obeying first order differential equations. Geometrically, the SO(7) covariant superspace constraints descend from a truncation of Witten's original linear system to particular one-parameter
families of light-like rays.
Received: 20 April 2000 / Accepted: 10 September 2000 相似文献
7.
In this paper we show that power-law inflation can be realized in non-minimal gravitational coupling of Yang–Mills field with
a general function of the Gauss–Bonnet invariant in the framework of Einstein gravity. Such a non-minimal coupling may appear
due to quantum corrections. We also discuss the non-minimal Yang–Mills-f(G) gravity in the framework of modified Gauss–Bonnet action which is widely studied recently. It is shown that both inflation
and late-time cosmic acceleration are possible in such a theory. 相似文献
8.
Jens Braun Astrid Eichhorn Holger Gies Jan M. Pawlowski 《The European Physical Journal C - Particles and Fields》2010,70(3):689-702
We study the nature of the confinement phase transition in d=3+1 dimensions in various non-abelian gauge theories with the approach put forward in Phys. Lett. B 684, 262 (2010). We compute an order-parameter potential associated with the Polyakov loop from the knowledge of full 2-point correlation
functions. For SU(N) with N=3,…,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase
transition in E(7) Yang–Mills theory also is of first order. We find that it is weaker than for SU(N). We show that this can be understood in terms of the eigenvalue distribution of the order parameter potential close to the
phase transition. 相似文献
9.
Ali H. Chamseddine 《Communications in Mathematical Physics》2001,218(2):283-292
The presence of a constant background antisymmetric tensor for open strings or D-branes forces the space-time coordinates
to be noncommutative. This effect is equivalent to replacing ordinary products in the effective theory by the deformed star
product. An immediate consequence of this is that all fields get complexified. The only possible noncommutative Yang–Mills
theory is the one with U(N) gauge symmetry. By applying this idea to gravity one discovers that the metric becomes complex. We show in this article
that this procedure is completely consistent and one can obtain complexified gravity by gauging the symmetry U(1,D−1) instead of the usual SO(1,D−1). The final theory depends on a Hermitian tensor containing both the symmetric metric and antisymmetric tensor. In contrast
to other theories of nonsymmetric gravity the action is both unique and gauge invariant. The results are then generalized
to noncommutative spaces.
Received: 1 June 2000 / Accepted: 27 November 2000 相似文献
10.
S. Habib Mazharimousavi M. Halilsoy Z. Amirabi 《General Relativity and Gravitation》2010,42(2):261-280
We find large classes of non-asymptotically flat Einstein–Yang–Mills–Dilaton and Einstein–Yang–Mills–Born–Infeld–Dilaton black
holes in N-dimensional spherically symmetric spacetime expressed in terms of the quasilocal mass. Extension of the dilatonic
YM solution to N-dimensions has been possible by employing the generalized Wu-Yang ansatz. Another metric ansatz, which aided
in finding exact solutions is the functional dependence of the radius function on the dilaton field. These classes of black
holes are stable against linear radial perturbations. In the limit of vanishing dilaton we obtain Bertotti–Robinson type metrics
with the topology of AdS
2×S
N–2. Since connection can be established between dilaton and a scalar field of Brans–Dicke type we obtain black hole solutions
also in the Brans–Dicke–Yang–Mills theory as well. 相似文献
11.
Kõta Yoshioka 《Communications in Mathematical Physics》1999,205(3):501-517
Recently, Minahan, Nemeschansky, Vafa and Warner computed partition functions for N = 4 topological Yang–Mills theory on rational
elliptic surfaces. In particular they computed generating functions of Euler characteristics of SU(2)-instanton moduli spaces. In mathematics, they are expected to coincide with those of Gieseker compactifications. In this
paper, we compute Euler characteristics of these spaces and show that our results coincide with theirs. We also check the
modular property of Z
SU
(2) and Z
SO
(3) conjectured by Vafa and Witten.
Received: 8 June 1998 / Accepted: 1 February 1999 相似文献
12.
C. Klimĉík 《Communications in Mathematical Physics》2001,217(1):203-228
A two dimensional gauge theory is canonically associated to every Drinfeld double. For particular doubles, the theory turns
out to be e.g. the ordinary Yang–Mills theory, the G/G gauged WZNW model or the Poisson σ-model that underlies the Kontsevich
quantization formula. We calculate the arbitrary genus partition function of the latter. The result is the q-deformation of the ordinary Yang–Mills partition function in the sense that the series over the weights is replaced by the
same series over the q-weights. For q equal to a root of unity the series acquires the affine Weyl symmetry and its truncation to the alcove coincides with the
Verlinde formula.
Received: 10 December 1999 / Accepted: 8 October 2000 相似文献
13.
Tatiana A. Ivanova Olaf Lechtenfeld Alexander D. Popov Thorsten Rahn 《Letters in Mathematical Physics》2009,89(3):231-247
We consider the Yang–Mills flow equations on a reductive coset space G/H and the Yang–Mills equations on the manifold
\mathbbR×G/H{\mathbb{R}\times G/H}. On non-symmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang–Mills equations to f4{\phi^4}-kink equations on
\mathbbR{\mathbb{R}}. Depending on the boundary conditions and torsion, we obtain solutions to the Yang–Mills equations describing instantons,
chains of instanton–anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on
\mathbbR×G/H{\mathbb{R}\times G/H}, dyon-type configurations are constructed as well. We also present explicit solutions to the Yang–Mills flow equations and
compare them with the Yang–Mills solutions on
\mathbbR×G/H{\mathbb{R}\times G/H}. 相似文献
14.
The study of superconductivity has been undertaken through the breaking of supersymmetric gauge theories which automatically
incorporate the condensation of monopoles and dyons leading to confining and superconducting phases. Constructing the effective
Lagrangian near a singularity in moduli space for N=2 supersymmetric theory with SU(2) gauge group, it has been shown that when a mass term is added to this Lagrangian, the N=2 Supersymmetry is reduced to N=1 supersymmetry yielding the dyonic condensation which leads to confinement and superconductivity as the consequence of generalized
Meissner effect. In the Coulomb phase of N=2 SU(3) Yang–Mills theory the gauge symmetry has been broken down to SU(2)×U(l) and it has been shown that on perturbing it by suitable tree-level superpotential this supersymmetry theory breaks to N=1 SU(2) Yang-Mills theory described by Higgs field in confining phase incorporating superconductivity. 相似文献
15.
Jussi Kalkkinen Antti J. Niemi 《The European Physical Journal C - Particles and Fields》1998,4(4):723-739
Recently there has been much progress in understanding confinement in the N=2 supersymmetric Yang–Mills theory. Here we shall
investigate how these results could be extended to explain color confinement in the ordinary Yang–Mills theory. In particular,
we inquire whether confinement in the N=2 theory can be related to color confinement in the ordinary Yang–Mills theory in
the framework of Parisi–Sourlas dimensional reduction. For this we study the partition function of the ordinary Yang–Mills
theory in different regimes. Our analysis reveals that an intimate connection indeed exists between these two approaches.
Received: 18 July 1997 / Revised version: 15 August 1997 / Published online: 23 February 1998 相似文献
16.
We study Bogomolny equations on ℝ2×?1. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions
with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform,
we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs
field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperk?hler manifolds
and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of ?=2 super Yang–Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius.
Received: 20 July 2000 / Accepted: 29 November 2000 相似文献
17.
James D. E. Grant 《Communications in Mathematical Physics》2010,296(2):405-428
We construct the most general reducible connection that satisfies the self-dual Yang–Mills equations on a simply-connected,
open subset of flat
\mathbbR4{\mathbb{R}^4}. We show how all such connections lie in the orbit of the flat connection on
\mathbbR4{\mathbb{R}^4} under the action of non-local symmetries of the self-dual Yang–Mills equations. Such connections fit naturally inside a larger
class of solutions to the self-dual Yang–Mills equations that are analogous to harmonic maps of finite type. 相似文献
18.
Manu P. Singh O. P. S. Negi B. S. Rajput 《International Journal of Theoretical Physics》2000,39(8):2029-2042
Breaking N = 2 SU(3) and N =2 SO(6) supersymmetric Yang–Mills theoriesto corresponding N = 1 theories by suitable tree-levelsuperpotentials, thehyperelliptic curves describing the Coulomb phase of these theories have beenobtained and it has been shown that the mass gap in the N = 1confining phaseof these theories vanishes when N = 1 parameters are properlytuned to approachthe highest critical points. 相似文献
19.
The Nekrasov conjecture predicts a relation between the partition function for N = 2 supersymmetric Yang–Mills theory and the Seiberg-Witten prepotential. For instantons on
\mathbbR4{\mathbb{R}^4}, the conjecture was proved, independently and using different methods, by Nekrasov-Okounkov and Nakajima-Yoshioka. We prove
a generalized version of the conjecture for instantons on noncompact toric surfaces. 相似文献
20.
Wei H. Ruan 《Communications in Mathematical Physics》2001,224(2):373-397
We give a rigorous proof of existence of infinitely many black hole solutions to the Einstein–Yang–Mills equations with gauge
group SU(3). In the case that the radius of event horizon is not too small, we show that there is a black hole solution for any possible
numbers of zeros of the two field variables.
Received: 23 October 2000 / Accepted: 30 January 2001 相似文献